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Question

(i) x4

(ii) x5/4

(iii) 1x5

(iv) 1x3/2

(v) 3x

(vi) 1x23

(vii) 32 log3 x

(viii) logx x

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Solution

(i)
x4dx=x4+14+1+C =x55+C

(ii)
x54dx=x54+154+1+C=49x94+C

(iii)
x-5dx=x-5+1-5+1+C=-14x-4+C=-14x4+C

(iv)
dxx3/2=x-3/2dx=x-32+1-32+1+C=x-12-12+C=-2x+C

(v)
3xdx=3xln 3+C

(vi)
dxx23=dxx2/3=x-2/3 dx=x-23+1-23+1+C=3x13+C

(vii)
32 log3xdx=3log3 x2dx=x2dx=x33+C

(viii)
logxx dx=1·dx=x+C

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